13.1 : Introduction to Nonparametric Statistics

Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.

One of the key advantages of nonparametric tests is their flexibility. They are more general and often simpler to apply, as they do not require data to meet certain criteria, such as homogeneity of variance or normal distribution. Additionally, nonparametric methods can handle a broader range of data types, including ordinal data (e.g., rankings or ratings) and nominal data (e.g., categories like eye color or gender), making them applicable to situations where parametric methods would be unsuitable.

Common examples of nonparametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Chi-square test, all of which can analyze data without requiring specific distributional assumptions. These tests are often easier to interpret since they rely on rank-ordering or contingency tables rather than estimating population parameters. Moreover, nonparametric methods are more robust to outliers, reducing the impact of extreme values that might otherwise skew results in parametric analysis. As a result, nonparametric methods are widely used in various fields ranging from social sciences and biology to economics and medicine.

Compared to parametric tests, nonparametric methods have lower sensitivity: they lose information by converting quantitative data into qualitative forms, like signs or ranks. For instance, recording ocean level changes as simply positive or negative signs instead of in millimeters reduces detail. Nonparametric tests also require more substantial evidence, such as larger sample sizes or greater differences, to reject the null hypothesis. When population parameters (mean, standard deviation) are available, parametric tests are generally preferred for their higher efficiency.